# Thermocouple

Model sensor that converts thermal potential difference into electrical potential difference

Sensors

## Description

The Thermocouple block represents a thermocouple using the standard polynomial parameterization defined in the NIST ITS-90 Thermocouple Database [1]. The voltage E across the device in mV is

E(mV) = c0 + c1*t + ... + cn*tn

where:

• ci is the ith element of the Coefficients [c0 c1 ... cn] parameter value.

• t is the temperature difference in degrees Celsius between the temperature at the thermal port A and the Reference temperature parameter value.

 Note:   The equation for voltage across the device as a function of temperature difference is defined in mV. The units of the voltage across the actual device is V.

The following equation describes the thermal behavior of the block:

`$Q={K}_{d}{t}_{c}\frac{dT}{dt}$`

where:

• T is the temperature at port A.

• Q is the net heat flow into port A.

• Kd is the Dissipation factor parameter value.

• tc is the Thermal time constant parameter value.

• dT/dt is the rate of change of the temperature.

To model the thermocouple in free space:

1. Connect the thermocouple to the B port of a Simscape™ Convective Heat Transfer block.

2. Connect the A port of the Convective Heat Transfer block to a Simscape Ideal Temperature Source block whose temperature is set to the ambient temperature.

3. Set the Area parameter of the Convective Heat Transfer block to an approximate area Anom.

4. Set the Heat transfer coefficient parameter of the Convective Heat Transfer block to Kd/Anom.

## Basic Assumptions and Limitations

The model is based on the following assumptions:

• The high-order polynomials this block uses are very sensitive to the number of significant figures used for computation. Use all available significant figures when specifying the Coefficients [c0 c1 ... cn] parameter.

• Coefficients [c0 c1 ... cn] are defined for use over a specified temperature range.

• This block does not include the additional exponential term that Type K thermocouples use when parameterized for t > 0.

## Dialog Box and Parameters

### Electrical Tab

Coefficients [c0 c1 ... cn]

The vector of coefficients c in the equation that describes voltage as a function of temperature. The default value is ```[ 0 0.0054031 1.2593e-05 -2.3248e-08 3.2203e-11 -3.315e-14 2.5574e-17 -1.2507e-20 2.7144e-24 ]```. This value specifies a Type S thermocouple, which is valid in the range -50 to 1064 degrees C.

 Note:   You can download parameters for other standard thermocouple types from the NIST database [1]. For information on how to do this, see the Simulink® Approximating Nonlinear Relationships: Type S Thermocouple example.

### Thermal Tab

Reference temperature

The temperature the block subtracts from the temperature at the thermal port in calculating the voltage across the device. The default value is `0` °C.

Thermal time constant

The time it takes the thermocouple temperature to reach 63% of the final temperature change when a step change in ambient temperature occurs. The default value is `1` s.

Dissipation factor

The thermal power required to raise the thermocouple temperature by one K. The default value is `0.001` W/K.

Initial temperature

The temperature of the thermocouple at the start of the simulation. The default value is `25` °C.

## Ports

The block has the following ports:

`A`

Thermocouple thermal port

`+`

Positive electrical port

`-`

Negative electrical port

## References

[1] NIST ITS-90 Thermocouple Database http://srdata.nist.gov/its90/main